Since the financial crisis cratered Wall Street, New York’s political class has focused on attracting other industries: social media, pickle-making, what have you. But the pols should lure new Wall Street jobs, too. New York could attract more of the world’s elite finance jobs — from places like London — if Gov. Cuomo and the city’s would-be mayors weren’t putting up a “not-welcome-here” sign.

Gotham has supposedly recovered since Wall Street went bust five years ago. New York has added back all the jobs it lost in the recession, and then some, as Mayor Bloomberg always reminds everyone.

With nearly 3.3 million private-sector workers, we’re 70,000 above where we were when all the banks almost failed. But New York is way behind when it comes to the financial industry. Before Bear Stearns needed the first of many bailouts five years ago this month, Wall Street had 188,900 jobs, according to state Comptroller Tom DiNapoli. Late last year, Wall Street had only 169,200 jobs. We’re still missing a whopping 10.4 percent.

Worse, a modest recovery has stalled. Wall Street got back up to 173,000 workers in 2010 and 2011. But it’s cutting back again. Goldman Sachs is naming new partners every two years, instead of every year — and firms from Citigroup to UBS are still chopping necks.

That matters, since Wall Street jobs pay out 23 percent of private wages in the city, DiNapoli notes — and 7 percent of city tax revenues (down from a 12 percent peak).

The truth is, New York won’t get its old finance jobs back. Large financial firms haven’t found a new business model — as anyone who watches JPMorgan Chase chief Jamie Dimon deal with the fallout of the “London Whale” loss can see. In fact, Wall Street’s employment is now back to 1997 levels — even before the earlier tech-stock bubble.

Some huge hedge funds, too, are directionless, at best. SAC Capital is losing clients who don’t want to wait and see if the firm’s insider-trading saga is over.

So who will create new Wall Street jobs? New York needs nimble new firms with fresh reputations and new ideas.

Look to the tech industry to look to finance. Much of finance is just information, and firms like Twitter are becoming experts at presenting and moving information.

But the pols should realize that New York is not competing with, say, Newark. It’s competing with the whole world for a bigger slice of a shrinking financial pie.

The good news is that our main competitor — London — is doing worse than we are. Since 2008, London has lost 28.6 percent of its financial jobs, according to the Centre for Economics and Business Research. And London has one huge disadvantage that New York doesn’t have: It is part of Continental Europe’s bureaucracy.

Europe’s latest idea is to cap bank bonuses so that they can’t exceed two times salary. London’s mayor, Boris Johnson, says this is “moronic.” But the European Parliament wants to punish London. The rule takes effect next year. Hedge-fund managers and smaller firms are terrified that lawmakers may expand the cap to them.

London has botched recovery in other ways, too. In 2010, it hiked the top income-tax rate from 40 percent to 50 percent. Since then, the government has admitted that the tax hike wasn’t bringing in the money it was supposed to — and that it might lose money. (Rich people could leave or earn less.)

But Britain then lowered the rate only to 45 percent, still higher than it was in 2009.

Leave it to New York, though, to look the gift horse in the mouth. Yes, it’s unreasonable to expect Cuomo to cut taxes. But he could have left them alone. Instead, he’s extending the “temporary” 28.9 percent tax hike he put in place a year and a half ago.

Thanks to higher federal tax rates, too, wealthy New Yorkers now pay 52 percent of their income in taxes — more than the rate London just cut.

Two mayoral candidates don’t think that’s a problem. City Comptroller John Liu and Public Advocate Bill de Blasio want to raise city taxes on the wealthy further.

London and the world’s financial elite are looking for friendlier climes, but it’s still winter here.

Nicole Gelinas is a contributing editor to the Manhattan Institute’s City Journal.